Question: A paintball court charges an initial entrance fee plus a fixed price per ball. The variable $p$ models the total price (in dollars) as a function of $n$, the number of balls used. $p=0.80n+5.50$ What is the entrance fee? $\$$
Solution: Before the paintball court charges for any balls, the number of balls, $n$, is $0$, and the total fee is equal to the entrance fee. We can calculate the fee: $\begin{aligned} p&=0.80n+5.50\\\\ p&=0.80(0)+5.50 \\\\ p&=0+5.50 \\\\ p &= 5.50 \end{aligned}$ The entrance fee is $\$5.50$.